Question: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 2x + 8$ and $ BC = 6x - 28$ Find $AC$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {2x + 8} = {6x - 28}$ Solve for $x$ $ -4x = -36$ $ x = 9$ Substitute $9$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 2({9}) + 8$ $ BC = 6({9}) - 28$ $ AB = 18 + 8$ $ BC = 54 - 28$ $ AB = 26$ $ BC = 26$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {26} + {26}$ $ AC = 52$